McGraw-Hill/Irwin McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. 9 9 Net Present Value and Other Investment Criteria
Jan 12, 2016
McGraw-Hill/IrwinMcGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
99Net Present Value
and Other Investment Criteria
Key Concepts and SkillsKey Concepts and Skills
Be able to compute payback and discounted payback and understand their shortcomings
Understand accounting rates of return and their shortcomings
Be able to compute the internal rate of return and understand its strengths and weaknesses
Be able to compute the net present value and understand why it is the best decision criterion
Chapter OutlineChapter Outline
Net Present Value The Payback Rule The Discounted Payback The Average Accounting Return The Internal Rate of Return The Profitability Index The Practice of Capital Budgeting
Good Decision CriteriaGood Decision Criteria
We need to ask ourselves the following questions when evaluating capital budgeting decision rules Does the decision rule adjust for the time
value of money? Does the decision rule adjust for risk? Does the decision rule provide information
on whether we are creating value for the firm?
Project Example InformationProject Example Information
You are looking at a new project and you have estimated the following cash flows: Year 0: CF = -165,000 Year 1: CF = 63,120; NI = 13,620 Year 2: CF = 70,800; NI = 3,300 Year 3: CF = 91,080; NI = 29,100 Average Book Value = 72,000
Your required return for assets of this risk is 12%.
Net Present ValueNet Present Value
The difference between the market value of a project and its cost
How much value is created from undertaking an investment? The first step is to estimate the expected future
cash flows. The second step is to estimate the required
return for projects of this risk level. The third step is to find the present value of the
cash flows and subtract the initial investment.
NPV – Decision RuleNPV – Decision Rule
If the NPV is positive, accept the project
A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.
Computing NPV for the ProjectComputing NPV for the Project
Using the formulas: NPV = 63,120/(1.12) + 70,800/(1.12)2 +
91,080/(1.12)3 – 165,000 = 12,627.42
Using the calculator: CF0 = -165,000; C01 = 63,120; F01 = 1; C02
= 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.41
Do we accept or reject the project?
Decision Criteria Test - NPVDecision Criteria Test - NPV
Does the NPV rule account for the time value of money?
Does the NPV rule account for the risk of the cash flows?
Does the NPV rule provide an indication about the increase in value?
Should we consider the NPV rule for our primary decision rule?
Calculating NPVs with a Calculating NPVs with a SpreadsheetSpreadsheet
Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well.
Using the NPV function The first component is the required return
entered as a decimal The second component is the range of cash
flows beginning with year 1 Subtract the initial investment after
computing the NPV
Payback PeriodPayback Period
How long does it take to get the initial cost back in a nominal sense?
Computation Estimate the cash flows Subtract the future cash flows from the initial
cost until the initial investment has been recovered
Decision Rule – Accept if the payback period is less than some preset limit
Computing Payback for the Computing Payback for the ProjectProject
Assume we will accept the project if it pays back within two years. Year 1: 165,000 – 63,120 = 101,880 still to
recover Year 2: 101,880 – 70,800 = 31,080 still to
recover Year 3: 31,080 – 91,080 = -60,000 project
pays back in year 3
Do we accept or reject the project?
Decision Criteria Test - PaybackDecision Criteria Test - Payback
Does the payback rule account for the time value of money?
Does the payback rule account for the risk of the cash flows?
Does the payback rule provide an indication about the increase in value?
Should we consider the payback rule for our primary decision rule?
Advantages and Disadvantages of Advantages and Disadvantages of PaybackPayback
Advantages Easy to understand Adjusts for
uncertainty of later cash flows
Biased toward liquidity
Disadvantages Ignores the time value
of money Requires an arbitrary
cutoff point Ignores cash flows
beyond the cutoff date Biased against long-
term projects, such as research and development, and new projects
Discounted Payback PeriodDiscounted Payback Period
Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis
Compare to a specified required period Decision Rule - Accept the project if it
pays back on a discounted basis within the specified time
Computing Discounted Payback for Computing Discounted Payback for the Projectthe Project
Assume we will accept the project if it pays back on a discounted basis in 2 years.
Compute the PV for each cash flow and determine the payback period using discounted cash flows Year 1: 165,000 – 63,120/1.121 = 108,643 Year 2: 108,643 – 70,800/1.122 = 52,202 Year 3: 52,202 – 91,080/1.123 = -12,627 project pays
back in year 3 Do we accept or reject the project?
Decision Criteria Test – Discounted Decision Criteria Test – Discounted PaybackPayback
Does the discounted payback rule account for the time value of money?
Does the discounted payback rule account for the risk of the cash flows?
Does the discounted payback rule provide an indication about the increase in value?
Should we consider the discounted payback rule for our primary decision rule?
Advantages and Disadvantages of Advantages and Disadvantages of Discounted PaybackDiscounted Payback
Advantages Includes time value of
money Easy to understand Does not accept
negative estimated NPV investments when all future cash flows are positive
Biased towards liquidity
Disadvantages May reject positive
NPV investments Requires an arbitrary
cutoff point Ignores cash flows
beyond the cutoff point Biased against long-
term projects, such as R&D and new products
Average Accounting ReturnAverage Accounting Return
There are many different definitions for average accounting return
The one used in the book is: Average net income / average book value Note that the average book value depends on
how the asset is depreciated.
Need to have a target cutoff rate Decision Rule: Accept the project if the
AAR is greater than a preset rate.
Computing AAR for the ProjectComputing AAR for the Project
Assume we require an average accounting return of 25%
Average Net Income: (13,620 + 3,300 + 29,100) / 3 = 15,340
AAR = 15,340 / 72,000 = .213 = 21.3%
Do we accept or reject the project?
Decision Criteria Test - AARDecision Criteria Test - AAR
Does the AAR rule account for the time value of money?
Does the AAR rule account for the risk of the cash flows?
Does the AAR rule provide an indication about the increase in value?
Should we consider the AAR rule for our primary decision rule?
Advantages and Disadvantages of Advantages and Disadvantages of AARAAR
Advantages Easy to calculate Needed information
will usually be available
Disadvantages Not a true rate of
return; time value of money is ignored
Uses an arbitrary benchmark cutoff rate
Based on accounting net income and book values, not cash flows and market values
Internal Rate of ReturnInternal Rate of Return
This is the most important alternative to NPV
It is often used in practice and is intuitively appealing
It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere
IRR – Definition and Decision IRR – Definition and Decision RuleRule
Definition: IRR is the return that makes the NPV = 0
Decision Rule: Accept the project if the IRR is greater than the required return
Computing IRR for the ProjectComputing IRR for the Project
If you do not have a financial calculator, then this becomes a trial and error process
Calculator Enter the cash flows as you did with NPV Press IRR and then CPT IRR = 16.13% > 12% required return
Do we accept or reject the project?
NPV Profile for the ProjectNPV Profile for the Project
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
Discount Rate
NP
V
IRR = 16.13%
Decision Criteria Test - IRRDecision Criteria Test - IRR
Does the IRR rule account for the time value of money?
Does the IRR rule account for the risk of the cash flows?
Does the IRR rule provide an indication about the increase in value?
Should we consider the IRR rule for our primary decision criteria?
Advantages of IRRAdvantages of IRR
Knowing a return is intuitively appealing It is a simple way to communicate the
value of a project to someone who doesn’t know all the estimation details
If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task
Summary of Decisions for the Summary of Decisions for the ProjectProject
SummaryNet Present Value Accept
Payback Period Reject
Discounted Payback Period
Reject
Average Accounting Return
Reject
Internal Rate of Return Accept
Calculating IRRs With A Calculating IRRs With A SpreadsheetSpreadsheet
You start with the cash flows the same as you did for the NPV
You use the IRR function You first enter your range of cash flows,
beginning with the initial cash flow You can enter a guess, but it is not necessary The default format is a whole percent – you
will normally want to increase the decimal places to at least two
NPV vs. IRRNPV vs. IRR
NPV and IRR will generally give us the same decision
Exceptions Non-conventional cash flows – cash
flow signs change more than once Mutually exclusive projects
Initial investments are substantially different Timing of cash flows is substantially different
IRR and Non-conventional Cash IRR and Non-conventional Cash FlowsFlows
When the cash flows change sign more than once, there is more than one IRR
When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation
If you have more than one IRR, which one do you use to make your decision?
Another Example – Non-Another Example – Non-conventional Cash Flowsconventional Cash Flows
Suppose an investment will cost $90,000 initially and will generate the following cash flows: Year 1: 132,000 Year 2: 100,000 Year 3: -150,000
The required return is 15%. Should we accept or reject the project?
NPV ProfileNPV Profile
($10,000.00)
($8,000.00)
($6,000.00)
($4,000.00)
($2,000.00)
$0.00
$2,000.00
$4,000.00
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
Discount Rate
NP
V
IRR = 10.11% and 42.66%
Summary of Decision RulesSummary of Decision Rules
The NPV is positive at a required return of 15%, so you should Accept
If you use the financial calculator, you would get an IRR of 10.11% which would tell you to Reject
You need to recognize that there are non-conventional cash flows and look at the NPV profile
IRR and Mutually Exclusive IRR and Mutually Exclusive ProjectsProjects
Mutually exclusive projects If you choose one, you can’t choose the other Example: You can choose to attend graduate school
at either Harvard or Stanford, but not both
Intuitively you would use the following decision rules: NPV – choose the project with the higher NPV IRR – choose the project with the higher IRR
Example With Mutually Exclusive Example With Mutually Exclusive ProjectsProjects
Period Project A
Project B
0 -500 -400
1 325 325
2 325 200
IRR 19.43%
22.17%
NPV 64.05 60.74
The required return for both projects is 10%.
Which project should you accept and why?
NPV ProfilesNPV Profiles
($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
$140.00
$160.00
0 0.05 0.1 0.15 0.2 0.25 0.3
Discount Rate
NP
V AB
IRR for A = 19.43%
IRR for B = 22.17%
Crossover Point = 11.8%
Conflicts Between NPV and IRRConflicts Between NPV and IRR
NPV directly measures the increase in value to the firm
Whenever there is a conflict between NPV and another decision rule, you should always use NPV
IRR is unreliable in the following situations Non-conventional cash flows Mutually exclusive projects
Profitability IndexProfitability Index
Measures the benefit per unit cost, based on the time value of money
A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value
This measure can be very useful in situations in which we have limited capital
Advantages and Disadvantages of Advantages and Disadvantages of Profitability IndexProfitability Index
Advantages Closely related to
NPV, generally leading to identical decisions
Easy to understand and communicate
May be useful when available investment funds are limited
Disadvantages May lead to incorrect
decisions in comparisons of mutually exclusive investments
Capital Budgeting In PracticeCapital Budgeting In Practice
We should consider several investment criteria when making decisions
NPV and IRR are the most commonly used primary investment criteria
Payback is a commonly used secondary investment criteria
Summary – Discounted Cash Flow CriteriaSummary – Discounted Cash Flow Criteria Net present value
Difference between market value and cost Take the project if the NPV is positive Has no serious problems Preferred decision criterion
Internal rate of return Discount rate that makes NPV = 0 Take the project if the IRR is greater than the required return Same decision as NPV with conventional cash flows IRR is unreliable with non-conventional cash flows or mutually exclusive
projects Profitability Index
Benefit-cost ratio Take investment if PI > 1 Cannot be used to rank mutually exclusive projects May be used to rank projects in the presence of capital rationing
Summary – Payback CriteriaSummary – Payback Criteria
Payback period Length of time until initial investment is recovered Take the project if it pays back within some specified
period Doesn’t account for time value of money and there is an
arbitrary cutoff period
Discounted payback period Length of time until initial investment is recovered on a
discounted basis Take the project if it pays back in some specified period There is an arbitrary cutoff period
Summary – Accounting CriterionSummary – Accounting Criterion
Average Accounting Return Measure of accounting profit relative to
book value Similar to return on assets measure Take the investment if the AAR
exceeds some specified return level Serious problems and should not be
used
Quick QuizQuick Quiz
Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9% and required payback is 4 years. What is the payback period? What is the discounted payback period? What is the NPV? What is the IRR? Should we accept the project?
What decision rule should be the primary decision method?
When is the IRR rule unreliable?
McGraw-Hill/IrwinMcGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
99End of Chapter
Comprehensive ProblemComprehensive Problem
An investment project has the following cash flows: CF0 = -1,000,000; C01 – C08 = 200,000 each
If the required rate of return is 12%, what decision should be made using NPV?
How would the IRR decision rule be used for this project, and what decision would be reached?
How are the above two decisions related?